一种基于选择性测量的自适应压缩感知方法

康荣宗; 田鹏武; 于宏毅

doi:10.7498/aps.63.200701

摘要

针对低信噪比条件下现有压缩感知系统重构性能严重恶化的问题，提出了一种基于选择性测量的自适应压缩感知结构. 首先推导并分析了经过压缩测量的噪声的统计特性及其对重构性能的影响；然后基于输出能量最小化准则，设计了一种压缩域投影滤波联合噪声检测的自适应感知器，感知获得噪声子空间的位置信息；进一步利用该信息构造选择性压缩测量矩阵，智能选择测量信号，同时“屏蔽”噪声分量，极大提高了压缩测量值的信噪比. 仿真结果表明，相对于现有压缩感知结构，选择性测量的压缩感知结构明显改善了含噪稀疏信号的重构性能，可更好地应用于吸波材料的前端特性分析、认知无线电的频谱感知等领域.

关键词:

Abstract

An adaptive compressed sensing architecture based on selective measure is proposed in this paper, in order to reduce the effects of non-sparse noise component on the performance of existing compressed sensing reconstruction algorithm. Firstly, in this paper we analyze and deduces the statistics characteristic of the measured noise and its influence on the reconstruction performance; then we propose a compressive-domain projection filter combined with iterative noise detector method to obtain the location information of noise subspace based on minimal output energy criteria; thirdly, we measure matrix adaptively with the location information, and focus on the signal subspace directly without sensing the noise component in analog part. Simulation results show that compared with the existing compressed sensing procedures, our method can obviously improve the performance of reconstruction of signals with noise, and can be used to perform the front-end spectrum analysis of absorbing materials and better detect the active channels in cognitive radio.

Keywords:

作者及机构信息

1.
信息工程大学信息工程学院, 郑州 450002

基金项目: 国家科技重大专项（批准号：2008ZX03006）资助的课题.

Authors and contacts

1.
College of Information Engineering, Information Engineering University, Zhengzhou 450002, China

Funds: Project supported by the National Science and Technology Major Projects of China (Grant No. 2008ZX03006).

参考文献

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施引文献

[1]	Sun L K, Cheng H F, Zhou Y J, Wang J 2012 Chin. Phys. B 21 055201
[2]	Zhou Y J, Pang Y Q, Cheng H F 2013 Chin. Phys. B 22 015201
[3]	Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[4]	Candes E J 2006 Proceedings of the International Congress of Mathematicians Madrid, Spain, August 22-30, 2006 p1433
[5]	Candes E J, Romberg J, Tao T 2006 IEEE Trans. Inform. Theory 52 489
[6]	Zhang J C, Fu N, Qiao L Y, Peng X Y 2014 Acta Phys. Sin. 63 030701 (in Chinese) [张京超, 付宁, 乔立岩, 彭喜元 2014 63 030701]
[7]	Sun B, Jiang J J 2011 Acta Phys. Sin. 60 110701 (in Chinese) [孙彪, 江建军 2011 60 110701]
[8]	Donoho D L, Tsaig Y 2006 Signal Process. 86 533
[9]	Tibshirani R 1996 J. Roy. Stat. Soc. B 58 267
[10]	Figueiredo M A T, Nowak R D, Wright S J 2007 IEEE J. Sel. Top. Sig. Proc. 1 586
[11]	Gorodnitsky I F, Rao B D 1997 IEEE Trans. Sig. Proc. 45 600
[12]	Rao B D, Engan K, Cotter S F 2003 IEEE Trans. Sig. Proc. 51 760
[13]	Neff R, Zakhor A 1997 IEEE Trans. Circ. Syst. Vide. 7 158
[14]	Needell D, Vershynin R 2010 IEEE Trans. Sel. Top. Sig. Proc. 4 310
[15]	Donoho D L, Tsaig Y, Drori I 2012 IEEE Trans. Inform. Theory. 58 1094
[16]	Davenport M A, Wakin M B 2010 IEEE Trans. Inform. Theory 56 4395
[17]	Tropp J A, Gilbert A C 2007 IEEE Trans. Inform. Theory 53 4655
[18]	Varadarajan B, Khudanpur S, Trac T D 2011 IEEE Sig. Proc. Lett. 18 27
[19]	Haupt J, Castro R M, Nowak R 2011 IEEE Trans. Inform. Theory 57 6222
[20]	Davenport M A, Arias-Castro E 2012 Proceedings of the IEEE International Symposium on Information Theory Massachusetts Ave, USA, July 1-6, 2012 p1827
[21]	Hanneke S 2011 Ann. Stat. 39 333
[22]	Koltchinskii V 2010 J. Mach. Learn. Res. 11 2457
[23]	Laska J N, Kirolos S, Duarte M F 2007 Proceedings of the IEEE International Symposium on Circuits and Systems New Orleans, Louisiana, USA, May 27-30, 2007 p1959
[24]	Baraniuk R 2007 IEEE Sig. Proc. Mag. 24 118
[25]	Donoho D L 2006 Commun. Pur. Appl. Math. 59 797
[26]	Eldar Y C, Kuppinger P, Bolcskei H 2010 IEEE Trans. Sig. Proc. 58 3042
[27]	Daubechies I, Devore R, Fornasier M, Gunturk C S 2010 Comm. Pure Appl. Math. 63 1

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